The interplay between time-reversal symmetry (TRS) and band topology plays a crucial role in topological states of quantum matter. In time-reversal-invariant (TRI) systems, the inversion of spin-degenerate bands with opposite parity leads to nontrivial topological states, such as topological insulators and Dirac semimetals. When the TRS is broken, the exchange field induces spin splitting of the bands. The inversion of a pair of spin-splitting subbands can generate more exotic topological states, such as quantum anomalous Hall insulators and magnetic Weyl semimetals. So far, such topological phase transitions driven by the TRS breaking have not been visualized. In this work, using angle-resolved photoemission spectroscopy, we have demonstrated that the TRS breaking induces a band inversion of a pair of spin-splitting subbands at the TRI points of Brillouin zone in ${\mathrm{EuB}}_6$, when a long-range ferromagnetic order is developed. The dramatic changes in the electronic structure result in a topological phase transition from a TRI ordinary insulator state to a TRS-broken topological semimetal (TSM) state. Remarkably, the magnetic TSM state has an ideal electronic structure, in which the band crossings are located at the Fermi level without any interference from other bands. Our findings not only reveal the topological phase transition driven by the TRS breaking, but also provide an excellent platform to explore novel physical behavior in the magnetic topological states of quantum matter.

中文翻译：

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EuB6中的时间逆对称打破驱动拓扑相变

时间反转对称性（TRS）和能带拓扑之间的相互作用在量子物质的拓扑状态中起着至关重要的作用。在时间反向不变（TRI）系统中，具有相反奇偶性的自旋简并能带的反转会导致非平凡的拓扑状态，例如拓扑绝缘体和狄拉克半金属。当TRS断开时，交换场会引起频带的自旋分裂。一对自旋分裂子带的倒置可以生成更多奇异的拓扑状态，例如量子异常霍尔绝缘体和磁性Weyl半金属。到目前为止，由TRS中断驱动的这种拓扑相变还没有可视化。在这项工作中，使用角分辨光发射光谱法，$B_6$，当开发了远距离铁磁有序时。电子结构的急剧变化导致拓扑结构从TRI普通绝缘体状态过渡到TRS断开的拓扑半金属（TSM）状态。值得注意的是，磁性TSM状态具有理想的电子结构，其中带交叉位于费米能级，而不受其他频带的干扰。我们的发现不仅揭示了由TRS断裂驱动的拓扑相变，而且为探索量子物质的磁性拓扑状态中的新物理行为提供了一个极好的平台。